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51.
Anne-Sophie de Suzzoni Nikolay Tzvetkov 《Archive for Rational Mechanics and Analysis》2014,212(3):849-874
We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast physics literature on related topics, we then study how much the Fourier modes of the solution at later times remain decorrelated. Our results are sensitive to the resonances associated with the dispersive relation and to the particular choice of the initial data. 相似文献
52.
We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable which can take values . Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc. 相似文献
53.
Nikolay K. Vitanov Zlatinka I. Dimitrova Kaloyan N. Vitanov 《Entropy (Basel, Switzerland)》2021,23(1)
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of to solution for arbitrary finite values of . Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM. 相似文献
54.
Dr. Vadim B. Krylov Dr. Alexey G. Gerbst Dmitry A. Argunov Dr. Andrey S. Dmitrenok Prof. Dr. Alexander S. Shashkov Prof. Dr. Zbigniew Kaczynski Prof. Dr. Johannes Huebner Prof. Dr. Otto Holst Prof. Dr. Nikolay E. Nifantiev 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(4):1749-1754
Enterococcus faecalis is one of most important nosocomial and often multi‐antibiotic resistant pathogens responsible for infections that are difficult to treat. Previously, a cell‐wall polysaccharide termed diheteroglycan (DHG) was isolated and characterized as a promising vaccine candidate. However, the configuration of its lactic acid (LA) residue attached to the galactofuranoside unit was not assessed, although it influences conformation of DHG chain in terms of biological recognition and immune evasion. This study proves the R configuration of the LA residue by means of chemical analysis, investigation of intramolecular NMR nuclear Overhauser effects and molecular dynamics simulations of native DHG and corresponding R and S models, which were obtained by using pyranoside‐into‐furanoside rearrangement. As alternative treatment and prevention strategies for E. faecalis are desperately needed, this discovery may offer the prospect of a synthetic vaccine to actively immunize patients at risk. 相似文献
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56.
In low- and medium-energy storage rings for synchrotron radiation (SR) production, it is necessary to use high-performance insertion devices (IDs) in order to meet the increasing demand for high X-ray flux to perform life science and material science, since the maximum beam energy and beam current cannot be changed in storage rings without major rebuilds of the accelerator systems. 相似文献
57.
58.
Larisa G. Shaidarova Larisa G. Popesku Nikolay A. Ulakhovich Herman C. Budnikov Nail G. Zabirov 《Phosphorus, sulfur, and silicon and the related elements》2013,188(1)
Abstract Crown-containing N-(thio)phosphoryl(thio)ureas are related to a class of NH-acids due to the presence of two acceptor-groups: (thio)phosphorylic and (thio)acylic. In agreement with structure of lariat ether, it was observed a stage corresponding to the step ejection of two H* ion on the potentiometric titration curve of ligand by alkaline. Calculated step ionization constants demonstrate that these compounds are weak acids with relative values of pK1 and pK2. 相似文献
59.
60.
Jordanka Petrova Snejana Momchilova Nikolay G. Vassilev 《Phosphorus, sulfur, and silicon and the related elements》2013,188(1-4):45-52
Abstract The interaction of Li-diethylbenzylphosphonate 1-Li with aldehydes 2 is studied at different reaction conditions, the corresponding β-hydroxyethanephosphonate 3 being isolated. It is found that in these cases the aldol stage of the HWE reaction is not stereoselective or threo isomers predominate. The elimination stage leads only to trans-alkene due to the electron and steric influence of the substituents at the phosphorus atom. 相似文献